Motivation

• Variations in quantitative traits are due to genetic and environmental factors
  
• Knowledge of the number, locations, effects, and identities of these factors can contribute to new biological insights
  • new drugs
    
  • improve breeding in agriculture
    
  • better understanding of natural selection

What is QTL mapping?

• A statistical method to identify genetic factors, or loci, that affect a quantitative trait
  
• Consider each marker, one at a time, and test whether it affects the trait

QTL mapping in two-parent crosses

• Cross two inbred lines to produce a F1 population
  
• Cross F1 subjects to produce a F2 population
  
• Genotype F2 subjects at many markers
  
• Phenotype F2 subjects for the trait of interest
  
• Test each marker for association with the trait

Multiparental populations

Motivation

• 10,000+ traits with RNA sequencing and mass spectrometry

• Quantitative trait locus mapping identifies genetic loci that affect measurable traits

• Multiparental populations offer high-resolution QTL mapping

• New analysis tools, such as a pleiotropy test for multiparental populations, are needed

Benefits of a new pleiotropy test

• Insights into genetic architecture

• Tool for expression trait hotspot dissection

• Complements mediation analysis

Jiang and Zeng (1995) test

• Two-parent crosses

• Applies to two traits that co-map

• \(H_0\): Pleiotropy

• \(H_A\): Two separate QTL

Jiang and Zeng (1995) test

• Perform a two-dimensional two-QTL scan

  • \(vec(Y) = Xvec(B) + vec(E)\)

  • Calculate likelihood at each ordered pair of positions

• Calculate likelihood ratio test statistic

Challenges in multiparental populations

• Complex patterns of relatedness

• Multiple founder lines

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.pull-right[.small[Photo by UNC Computational Genetics]]

Test procedure

• Perform a two-dimensional two-QTL scan

  • \(vec(Y) = Xvec(B) + vec(G) + vec(E)\)

  • Calculate likelihood at each ordered pair of positions

• Calculate likelihood ratio test statistic

Test procedure

• Test statistic: \[- \log_{10} \frac{\max (\text{likelihood under pleiotropy})}{\max (\text{likelihood for separate QTL})}\]

• Parametric bootstrap to get a \(p\)-value

Application

• Logan et al. (2013) and Recla et al. (2014) studied 261 Diversity Outbred mice

• Measured about two dozen behavioral traits

• Two traits map to Chr 8:

  • “hot plate latency” (57 cM)

  • “percent time in light” (55 cM)

Percent time in light

Hot plate latency

LOD definitions

• \[LOD(\lambda_1, \lambda_2) = ll_{10}(\lambda_1, \lambda_2) - \max_{\lambda} ll_{10}(\lambda, \lambda)\]

• \[\text{profile LOD}_{\text{trait 1}}(\lambda_1) = \max_{\lambda_2}LOD(\lambda_1, \lambda_2)\]

• \[LOD_p(\lambda) = ll_{10}(\lambda, \lambda) - \max_{\lambda} ll_{10}(\lambda, \lambda)\]

Profile LOD

Test results

• \(\log_{10} \Lambda = 1.2\)

• \(p = 0.11\) (1000 bootstrap samples)

Conclusions

• \(\uparrow\) Pleiotropy test statistics
  • \(\uparrow\) Interlocus distance
  • \(\uparrow\) Univariate LOD

qtl2pleio R package

• Functions for \(d\)-variate, \(d\)-QTL scan & profile LOD plots

• Uses C++ for matrix calculations (via Rcpp and RcppEigen)

• Uses gemma2 R implementation of GEMMA EM algorithm for multivariate random effects

• Unit tests, vignettes, and version control

Summary

1. Background
   
2. Methods
   
3. Applications
   1. Pleiotropy testing and mediation analysis
      
   2. Power in pleiotropy testing
      
   3. Microbiome case study
      
4. Software
   
5. Conclusions

References

Jiang, C. and Z. Zeng (1995). “Multiple trait analysis of genetic mapping for quantitative trait loci.” In: Genetics 140.3, pp. 1111-1127.

Logan, R. W., R. F. Robledo, et al. (2013). “High-precision genetic mapping of behavioral traits in the diversity outbred mouse population”. In: Genes, Brain and Behavior 12.4, pp. 424-437.

Recla, J. M., R. F. Robledo, et al. (2014). “Precise genetic mapping and integrative bioinformatics in Diversity Outbred mice reveals Hydin as a novel pain gene”. In: Mammalian genome 25.5-6, pp. 211-222.